PERIODIC AND SUBHARMONIC SOLUTIONS FOR DUFFING EQUATION WITH A SINGULARITY

被引：34

作者：

Cheng, Zhibo ^{[1
]}

Ren, Jingli ^{[1
]}

机构：

[1] Zhengzhou Univ, Dept Math, Zhengzhou 450001, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2012年 / 32卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Duffing equation; harmonic and subharmonic solution; superlinear; singularity; Poincare-Birkhoff twist theorem; 2ND-ORDER DIFFERENTIAL-EQUATIONS; MULTIPLICITY; EXISTENCE;

D O I：

10.3934/dcds.2012.32.1557

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to the existence and multiplicity of periodic and subharmonic solutions for a superlinear Duffing equation with a singularity. In this manner, various preceding theorems are improved and sharpened. Our proof is based on a generalized version of the Poincare-Birkhoff twist theorem.

引用

页码：1557 / 1574

页数：18

共 17 条

[1] T-PERIODIC SOLUTIONS FOR SOME 2ND-ORDER DIFFERENTIAL-EQUATIONS WITH SINGULARITIES [J].

DELPINO, M ;

MANASEVICH, R ;

MONTERO, A .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1992, 120 :231-243

[2] INFINITELY MANY T-PERIODIC SOLUTIONS FOR A PROBLEM ARISING IN NONLINEAR ELASTICITY [J].

DELPINO, MA ;

MANASEVICH, RF .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1993, 103 (02) :260-277

[3] PERIODIC-SOLUTIONS OF DUFFINGS EQUATIONS WITH SUPERQUADRATIC POTENTIAL [J].

DING, T ;

ZANOLIN, F .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1992, 97 (02) :328-378

[4]

Ding T., 2004, Applications of Qualitative Methods of Ordinary Differential Equations

[5] EXISTENCE AND MULTIPLICITY RESULTS FOR PERIODIC-SOLUTIONS OF SEMILINEAR DUFFING EQUATIONS [J].

DING, TR ;

IANNACCI, R ;

ZANOLIN, F .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1993, 105 (02) :364-409

[6] A GENERALIZATION OF THE POINCARE-BIRKHOFF THEOREM [J].

DING, WY .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 88 (02) :341-346

[7] SUBHARMONIC SOLUTIONS FOR SOME 2ND-ORDER DIFFERENTIAL-EQUATIONS WITH SINGULARITIES [J].

FONDA, A ;

MANASEVICH, R ;

ZANOLIN, F .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1993, 24 (05) :1294-1311

[8] Radially symmetric systems with a singularity and asymptotically linear growth [J].

Fonda, Alessandro ;

Toader, Rodica .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (07) :2485-2496

[9] PERIODIC-SOLUTIONS OF SOME LIENARD EQUATIONS WITH SINGULARITIES [J].

HABETS, P ;

SANCHEZ, L .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1990, 109 (04) :1035-1044

[10] Multiplicity of positive periodic solutions to superlinear repulsive singular equations [J].

Jiang, DQ ;

Chu, JF ;

Zhang, M .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2005, 211 (02) :282-302

← 1 2 →